Knowledge that Transforms

Conventional Bayesian theory of choice under uncertainty, subjective expected utility theory, fails to satisfy the properties of admissibility and existence of well-defined conditional probabilities; weakly dominated acts may be chosen, and the usual definition of conditional probabilities applies only to nonnull events. This paper develops a non-Archimedean variant of subjective expected utility where decisionmakers have lexicographic beliefs. This generalization can be made to satisfy admissibility and yield well-defined conditional probabilities and at the same time allow for "null" events. Copyright 1991 by The Econometric Society.

We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure-strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimen- sional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristics approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper (Caplin and Nalebuff (1991)) introduces these theorems and develops the application to super-majority voting rules. WE PRESENT A NEW APPROACH to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result is that there exists a pure-strategy price equilibrium for any number of firms producing any set of products. In addition to the proof of existence, we provide conditions for uniqueness. Our model both unites diverse strands of the earlier literature and opens up uncharted areas for future analysis. In particular, we expand the traditional one-dimensional framework to allow for multi-dimen- sional product differentiation. Our approach involves twin restrictions on consumer preferences: one on individuals' preferences, the other on the distribution of preferences across society. These are generalizations of the restrictions supporting 64%-majority rule presented in Caplin and Nalebuff (1988). To prove existence, we apply a new technique of aggregation. This technique is valuable in a variety of other problems. In the companion paper, we use the aggregation result to generalize our earlier work on 64%-majority rule and to characterize the relationship between the distribution of human capital and the distribution of income (Caplin and Nalebuff (1991)). There are additional applications in statistics and in search theory. We begin with a brief review of the early literature on imperfect competition, describing in more detail the existence problem and previous solutions. Section 3 presents our twin assumptions, and shows that they cover many standard cases. In Section 4, we introduce the aggregation theorem and use it in the analysis of demand functions. The proof of existence of equilibrium is in Section

We specify a model of municipal labor demand when resource flows available to the municipality are uncertain. The model allows us to test the hypothesis that employment decisions are rational in the sense that they incorporate all available information at the time that the decisions are made. We find that, for our sample of communities, on the whole one cannot reject the hypothesis that labor demand is consistent with intertemporal utility maximization under uncertainty. However, small and large communities exhibit different behavior. The employment decisions of small communities are consistent with the model, while those of large communities are not.

Unionization affects cost of production through compensation premia, technology shifts, and deviations from the least-cost combination of inputs. The first two are familiar, but the last is not. This article distinguishes the three effects, illustrates the factor-use effect, and suggests that it may resolve several apparent inconsistencies: union-induced cost effects appear larger than those implied by union compensation and productivity differentials; union compensation and productivity differentials suggest a larger effect on labor intensity of output than is observed; and employers complain that union work rules reduce productivity when there is little evidence that this is so.

A standard efficient-contracts model of employment determination in a unionized labor market is contrasted with a naive model of labor supply and demand that allows for the possibility of monopsony in the market for public school teachers. The standard model is consistent with the data and suggests that employment contracts are strongly efficient, but a more surprising result is that the simple supply/demand model is not rejected by the data either. Estimates of the latter suggest that the demand for teachers is inelastic and that the supply curve is slightly upward sloping, rather than perfectly elastic, at the union wage.